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Temgoua, Anatole, Malong, Yannick, Mbang, Joseph, Bowong, Samuel. (1397). Global properties of a tuberculosis model with lost sight and multi-compartment of latents. فیزیولوژی و بیوتکنولوژی آبزیان, 6(1), 47-76. doi: 10.22124/jmm.2018.2775
Anatole Temgoua; Yannick Malong; Joseph Mbang; Samuel Bowong. "Global properties of a tuberculosis model with lost sight and multi-compartment of latents". فیزیولوژی و بیوتکنولوژی آبزیان, 6, 1, 1397, 47-76. doi: 10.22124/jmm.2018.2775
Temgoua, Anatole, Malong, Yannick, Mbang, Joseph, Bowong, Samuel. (1397). 'Global properties of a tuberculosis model with lost sight and multi-compartment of latents', فیزیولوژی و بیوتکنولوژی آبزیان, 6(1), pp. 47-76. doi: 10.22124/jmm.2018.2775
Temgoua, Anatole, Malong, Yannick, Mbang, Joseph, Bowong, Samuel. Global properties of a tuberculosis model with lost sight and multi-compartment of latents. فیزیولوژی و بیوتکنولوژی آبزیان, 1397; 6(1): 47-76. doi: 10.22124/jmm.2018.2775

Global properties of a tuberculosis model with lost sight and multi-compartment of latents

Journal of Mathematical Modeling
مقاله 3، دوره 6، شماره 1، مهر 2018، صفحه 47-76    اصل مقاله (452.45 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2018.2775
نویسندگان
Anatole Temgoua1؛ Yannick Malong1؛ Joseph Mbang2؛ Samuel Bowong* 3
1Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon
2Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon
3Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon
چکیده
A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $\mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $\mathcal{R}_0$, this state can be either endemic ($\mathcal{R}_0> 1$), or infection-free ($\mathcal{R}_0\leq 1$). The global asymptotic stability of equilibria is established using Lyapunov functions that combine quadratic, Volterra-type and linear functions. The theory is supported by numerical simulations.
کلیدواژه‌ها
TB؛ mathematical models؛ basic reproduction number؛ Stability
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